Rigify Rig moves twice as fast as the Armature Root bone after parenting everything to the Root
It looks like you might have two armature nodes where you only want one. Look into this possibility. In my experience, double transformation weirdness can often be traced to having an extra armature node that was created accidentally. This often happens by the old armature node not being deleted before trying to rebind a mesh. An armature node will be created every time you try to bind a mesh, even if that mesh already has an armature node attached to it.